2 weeks is not safe. Realistically, they should be consumed in 2-4 days. You can probably push it a day or two longer, but by simply exposing the yolk and whites to air, you're providing bacteria a place to grow. Eggs are full of things that bacteria like to eat, and while most of what grows there will be harmless, some of it won't.
I also think that you'd find mold growing within 2 weeks, so that's kind of a moot point.
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